Question: Simplify the following expression: $ y = \dfrac{6}{-2t - 8} - \dfrac{-9}{2} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{6}{-2t - 8} \times \dfrac{2}{2} = \dfrac{12}{-4t - 16} $ Multiply the second expression by $\dfrac{-2t - 8}{-2t - 8}$ $ \dfrac{-9}{2} \times \dfrac{-2t - 8}{-2t - 8} = \dfrac{18t + 72}{-4t - 16} $ Therefore $ y = \dfrac{12}{-4t - 16} - \dfrac{18t + 72}{-4t - 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{12 - (18t + 72) }{-4t - 16} $ Distribute the negative sign: $y = \dfrac{12 - 18t - 72}{-4t - 16}$ $y = \dfrac{-18t - 60}{-4t - 16}$ Simplify the expression by dividing the numerator and denominator by -2: $y = \dfrac{9t + 30}{2t + 8}$